TRANSMISSION WILL NOT ENGAGE

PICKED UP A COROLLA WITH WHAT WE THOUGHT WAS A BAD TRANSMISSION, GOT IT HOME CHARGED THE BATTERY AND TRIED IT IT DROVE AROUND THE BLOCK I LET IT WARM UP WHILE TRYING THE A/C THEN TRIED AGAIN MADE IT HALFWAY THEN NOTHING NO FORWARD NO REVERSE NOTHING, BOUGHT ANOTHER ONE WITH A ROD KNOCK BUT GOOD TRANNY DROVE IT HOME ( SLOWLY, ABOUT 15 MILES) SWAPPED IN THE ENGINE FROM THE OTHER CAR TO THIS ONE AND THE SAME THING HAPPENED GOT AROUND THE BLOCK AND THEN NOTHING NO CHECK ENGINE LIGHTS BUT WE SUSPECT THAT IT HAS TO BE SOME KIND OF SENSOR TRIED SWITCHING WATER TEMP SENSORS FROM OTHER ENGINE STILL NOTHING SHOULD I TRY THE ONES OFF THE INTAKE?

You would have to use an A131L trans from a 89-92 Toyota Corolla or Geo Prizm (if 3 speed automatic).

Check the TV cable adjustment, it connects from the throttle body cam to the trans. If broken or out of adjustment the trans will slip, since this controls hydraulic pressure to trans.
If broken do not drive the car until the TV cable is fixed, as it will cause an internal leak and the trans. Will have to be rebuilt.

Thanks, the donor car was same year corolla even the same color but the trans is not slipping it has nothing we disconnected the lines to the radiator and we have no fluid flowing out. We changed the filter refilled with new fluid and still nothing.